The technique in the link you posted is an inefficient workaround presented by someone that does not fully understand the reason that a motion path does not precisely follow a vector (mask or shape) path. Let me explain the problem and give you the solution.
Mask paths are always created in layer space before any layer transformations. If you want a motion path to follow a mask path precisely then the layer with the mask or the shape layer with the path cannot have any changes to the Layer>Transform>Position, Scale, or Rotation properties*. It's as simple as that. Reset all of the Layer>Transform properties, draw a path on the layer (or shape layer) then copy and paste and the motion path will always line up on top of the vector path.
*If the layer is 3D you can rotate it in X or Y but never in Z.
The solution is to use a solid or a new shape layer, draw your path on the layer before you move or scale it, then copy the path and paste it to any parameter that has a position value. The motion path will always be in the XY plane even if the layer is 3D. There is a workaround if you need the motion path to be on a different plane. All you have to do is paste the motion path to a 3D layer's position property, add a 3D null, parent the moving 3D layer to the null, then rotate the null.
Some folks think this is an extra step but when I am going to copy a path and paste it to a motion path I always set a path keyframe, cut the keyframe (Ctrl/Cmnd + x) then select the layer I want to move and press Alt/Option + p to set a position keyframe and immediately paste Ctrl/Cmnd + v. Using this technique you will never have a problem turning the vector path into a motion path.
Here's a quick tutorial I did a long time ago that shows how to draw a vector path on a 3D layer and then turn that into a motion path for a camera. Notice that the reference layer that I rotated in X was not scaled or rotated in Z. That's why the technique works.
https://youtu.be/YyPMYK7ROYU